Atoms ,Molecules and Nuclei
Prepared by physics dept
Sangita Holkar
The Atom
The atom consists of two parts:
1. The nucleus which contains:
2. Orbiting electrons.
protons
neutrons
All matter is made up of elements (e.g. carbon,
hydrogen, etc.).
The smallest part of an element is called an atom.
Atom of different elements contain different numbers of
protons.
The mass of an atom is almost entirely due to the
number of protons and neutrons.
The Atom
XA
Z
Mass number
Atomic number
Element symbol
= number of protons + number of neutrons
= number of protons
XA
Z
A = number of protons + number of neutrons
Z = number of protons
A – Z = number of neutrons
Number of neutrons = Mass Number – Atomic Number
U235
92U
238
92
There are many types of uranium:
A
Z
Number of protons
Number of neutrons
A
Z
Number of protons
Number of neutrons
U235
92U
238
92
There are many types of uranium:
Isotopes of any particular element contain the same
number of protons, but different numbers of neutrons.
A 235
Z 92
Number of protons 92
Number of neutrons 143
A 238
Z 92
Number of protons 92
Number of neutrons 146
Most of the isotopes which occur naturally are stable.
A few naturally occurring isotopes and all of the man-
made isotopes are unstable.
Unstable isotopes can become stable by releasing
different types of particles.
This process is called radioactive decay and the
elements which undergo this process are called
radioisotopes/radionuclides.
Radioactive decay results in the emission of either:
• an alpha particle (a),
• a beta particle (b),
• or a gamma ray(g).
Radioactive Decay
An alpha particle is identical to that of a helium nucleus.
It contains two protons and two neutrons.
Alpha Decay
XA
ZY
A - 4
Z - 2+ He
4
2
Alpha Decay
unstable atom
more stable atom
alpha particle
Alpha Decay
Ra226
88
Rn222
86
He4
2
XA
ZY
A - 4
Z - 2+ He
4
2
Ra226
88Rn
222
86+ He
4
2
Alpha Decay
Rn222
86He
4
2+Po
218
84He
4
2
Rn222
86+Y
A
ZHe
4
2
Alpha Decay
He4
2U
234
92+Th
230
90He
4
2
XA
Z+Th
230
90He
4
2
Alpha Decay
Th230
90+Y
A
ZHe
4
2
Alpha Decay
He4
2+Ra
226
88He
4
2Th
230
90
XA
Z+Pb
214
82He
4
2
Alpha Decay
He4
2+Pb
214
82He
4
2Po
218
84
Beta Decay
A beta particle is a fast moving electron which is
emitted from the nucleus of an atom undergoing
radioactive decay.
Beta decay occurs when a neutron changes into a
proton and an electron.
Beta Decay
As a result of beta decay, the nucleus has one less
neutron, but one extra proton.
The atomic number, Z, increases by 1 and the mass
number, A, stays the same.
Beta Decay
Po218
84
b0
-1
At218
85
XA
ZY
A
Z + 1+ b
0
-1
Beta Decay
Po218
84Rn
218
85+ b
0
-1
Th234
90Y
A
Z+ b
0
-1
Beta Decay
Th234
90Pa
234
91+ b
0
-1
XA
ZPb
210
82+ b
0
-1
Beta Decay
Tl210
81Pb
210
82+ b
0
-1
Bi210
83Y
A
Z+ b
0
-1
Beta Decay
Bi210
83Po
210
84+ b
0
-1
XA
ZBi
214
83+ b
0
-1
Beta Decay
Pb214
82Bi
214
83+ b
0
-1
Gamma Decay
Gamma rays are not charged particles like a and b
particles.
Gamma rays are electromagnetic radiation with high
frequency.
When atoms decay by emitting a or b particles to form a
new atom, the nuclei of the new atom formed may still
have too much energy to be completely stable.
This excess energy is emitted as gamma rays (gamma ray
photons have energies of ~ 1 x 10-12 J).
Radioactivity:
Lead
Box
Radioactive
substance
α
β
γ
-
-
-
--
-
-
--
-
-
+
+
+
+
+
+
+
+
+
+
Radioactivity is the phenomenon of emitting
alpha, beta and gamma radiations
spontaneously.
Soddy’s Displacement Law:
1. ZYA Z-2Y
A-4α
2. ZYA Z+1Y
Aβ
3. ZYA ZYA (Lower energy)
γ
Rutherford and Soddy’s Laws of Radioactive Decay:
1. The disintegration of radioactive material is purely a random process and
it is merely a matter of chance. Which nucleus will suffer disintegration, or
decay first can not be told.
2. The rate of decay is completely independent of the physical composition
and chemical condition of the material.
3. The rate of decay is directly proportional to the quantity of material
actually present at that instant. As the decay goes on, the original material
goes on decreasing and the rate of decay consequently goes on
decreasing.
If N is the number of radioactive atoms present at any instant, then the rate of
decay is,
dt
dN- α N or
dN
dt- = λ N
where λ is the decay constant or the disintegration constant.
Rearranging,
N
dN= - λ dt
Integrating, loge N = - λ t + C where C is the integration constant.
If at t = 0, we had N0 atoms, then
loge N0 = 0 + C
loge N - loge N0 = - λ t
or loge (N / N0) = - λ t
orN
= e- λt
N0
or N = N0 e- λ t No
. o
f ato
ms (
N) N0
N0/2
N0/4
N0/8N0/16
Time in half lives
0 T 2T 3T 4T
Radioactive Disintegration Constant (λ):
According to the laws of radioactive decay,
N
dN= - λ dt
If dt = 1 second, then
N
dN= - λ
Thus, λ may be defined as the relative number of atoms decaying per second.
Again, since N = N0 e- λ t
And if, t = 1 / λ, then N = N0 / e
orN0
N=
e
1
Thus, λ may also be defined as the reciprocal of the time when N / N0 falls to 1 / e.
Half – Life Period:
Half life period is the time required for the disintegration of half of the amount
of the radioactive substance originally present.
If T is the half – life period, then
N0
N=
2
1= e - λ T
e λ T = 2
(since N = N0 / 2)
λ T = loge 2 = 0.6931
T =λ
0.6931
T
λ = 0.6931
or
Time t in which material changes from N0 to N:
t = 3.323 T log10 (N0 / N)
Number of Atoms left behind after n Half – Lives:
N = N0 (1 / 2)t/TN = N0 (1 / 2)n or
Units of Radioactivity:
1. The curie (Ci): The activity of a radioactive substance is said to be one
curie if it undergoes 3.7 x 1010 disintegrations per second.
1 curie = 3.7 x 1010 disintegrations / second
2. The rutherford (Rd): The activity of a radioactive substance is said to be
one rutherford if it undergoes 106 disintegrations per second.
1 rutherford = 106 disintegrations / second
3. The becquerel (Bq): The activity of a radioactive substance is said to be
one becquerel if it undergoes 1 disintegration per second.
1 becquerel = 1 disintegration / second
1 curie = 3.7 x 104 rutherford = 3.7 x 1010 becquerel
Nuclear Fission:
Nuclear fission is defined as a type of nuclear disintegration in which a heavy
nucleus splits up into two nuclei of comparable size accompanied by a
release of a large amount of energy.
0n1 + 92U
235 → (92U236) → 56Ba141 + 36Kr92 +30n
1 + γ (200 MeV)
Chain Reaction:
n = 1
N = 1
n = 2
N = 9
n = 3
N = 27
Neutron (thermal) 0n1
Uranium 92U235
Barium 56Ba141
Krypton 36Kr92
n = No. of fission stages
N = No. of Neutrons
N = 3n
Chain Reaction:
n = 1
N = 1
n = 2
N = 9
n = 3
N = 27
Critical Size:
For chain reaction to occur, the
size of the fissionable material
must be above the size called
‘critical size’.
A released neutron must travel
minimum through 10 cm so that it
is properly slowed down (thermal
neutron) to cause further fission.
If the size of the material is less
than the critical size, then all the
neutrons are lost.
If the size is equal to the critical
size, then the no. of neutrons
produced is equal to the no. of
neutrons lost.
If the size is greater than the
critical size, then the reproduction
ratio of neutrons is greater than 1
and chain reaction can occur.
Nuclear Fusion:Nuclear fusion is defined as a type of nuclear reaction in which two lighter
nuclei merge into one another to form a heavier nucleus accompanied by a
release of a large amount of energy.
Energy Source of Sun:
Proton – Proton Cycle:
1H1 + 1H
1 → 1H2 + 1e
0 + 0.4 MeV
1H1 + 1H
2 → 2He3 + 5.5 MeV
2He3 + 2He3 → 2He4 + 2 1H1 + 12.9 MeV
Carbon - Nitrogen Cycle:
6C12 + 1H
1 → 7N13 + γ (energy)
7N13 → 6C
13 + 1e0 (positron)
Energy Source of Star:
6C13 + 1H
1 → 7N14 + γ (energy)
7N14 + 1H
1 → 8O15 + γ (energy)
8O15 → 7N
15 + 1e0 (positron)
7N15 + 1H
1 → 6C12 + 2He4 + γ (energy)
End of Atomic Nucleus
Nature of a wave
• A wave is described by frequency , wavelength , phase velocity u and intensity I
• A wave is spread out and occupies a relatively large region of space
Nature of a particle
• A particle is specified by mass m, velocity v, momentum p, and energy E
• A particle occupies a definite position in space.
In order for that it must be small
Light
• Interference and Diffraction experiments showed the wave nature of light
• Blackbody radiation and Photoelectric effectcan be explained only by considering light as a stream of particles
So is light a wave or a particle
?
How are they related?
E = h
• E– energy of the photon
• – frequency of the wave
• h– plank's constant
p=h/
p – momentum of the particle
- wavelength of the photon
40
DE BROGLIE HYPOTHESIS
LOUIS DE BROGLIE
“ If radiation which is basically a wave can exhibitparticle nature under certain circumstances, andsince nature likes symmetry, then entities whichexhibit particle nature ordinarily, should also exhibitwave nature under suitable circumstances”
In the Year 1924 Louis de Brogliemade the bold suggestion
The reasoning used might be paraphrased as follows
1. Nature loves symmetry2. Therefore the two great entities, matter and
energy, must be mutually symmetrical3. If energy (radiant) is undulatory and/or
corpuscular, matter must be corpuscular and/or undulatory
The de Broglie Hypothesis
• If light can act like a wave sometimes and like a particle at other times, then all matter, usually thought of as particles, should exhibit wave-like behaviour
• The relation between the momentum and the wavelength of a photon can be applied to material particles also
Prince Louis de Broglie (1892-1987)
de Broglie Wavelength
Relates a particle-like property (p) to a wave-like property ()
h
mv
43nm
VoltsVforthus
nmVV
getweeandmhforngsubstituti
meV
h
mE
hThen
VdifferencePotentialabydaccelerate
EEnergyKineticwithelectronanfor
mv
h
p
hwavelengthBrogliede
1226.0100
226.1
100
226.1
10602.11011.92
10625.6
,,
22
''
''
particle theof velocity theis v
particle theof mass theis m
Constant sPlanck' ish
1931
34
DE BROGLIE WAVELENGTH
The Wave associated with the matter particle is called Matter Wave.The Wavelength associated is called de Broglie Wavelength.
E hf
The frequency
• De Broglie postulated that all particles satisfy Einstein’s relation
ƒE
h
In other words,
Example: de Broglie wavelength of an electron
Mass = 9.11 x 10-31 kgSpeed = 106 m / sec
m10287m/sec) kg)(10 10(9.11
secJoules10636 10
631
34
.
.
This wavelength is in the region of X-rays
Example: de Broglie wavelength of a ball
• Mass = 1 kgSpeed = 1 m / sec
m10636m/sec) kg)(1 (1
secJoules10636 3434
..
Theoretical implication – The Bohr postulate
• Consider standing waves produced in a stretched string tied at two ends
Condition for these standing waves is that the length
of the string should be integral multiple of /2
The Diffraction
X-rays electrons
The diffraction patterns are similar because electrons have similar wavelengths to X-rays
Wave-like Behaviour of Matter
• Evidence: – electron diffraction
– electron interference (double-slit experiment)
• Also possible with more massive particles, such as neutrons and a-particles
• Applications:– Bragg scattering
– Electron microscopes
– Electron- and proton-beam lithography
particle wave function
Wave-Particle Duality
Wave Function
• Completely describes all the properties of agiven particle
• Called y y (x,t); is a complex function of position x and time t
particle wave function
Wave-Particle Duality
53
PHASE VELOCITY
Phase velocity: The velocity with which a wave travels is called Phase
velocity or wave velocity. It is denoted by vp. It is given by
v
cv p
2
Where c = velocity of light and v = is velocity of the particle.
The above equation gives the relationship between the phase velocity and
particle velocity.
It is clear from the above equation that, Phase velocity is not only greater
than the velocity of the particle but also greater than the velocity of light,
which can never happen. Therefore phase velocity has no physical
meaning in case of matter waves. Thus a concept of group velocity was
introduced.
54
GROUP VELOCITY
Since phase velocity has no meaning, the concept of group velocity was
introduced as follows.
“ Matter wave is regarded as the resultant of the superposition of largenumber of component waves all traveling with different velocities. The resultantis in the form of a packet called wave packet or wave group. The velocity withwhich this wave group travels is called group velocity.” The group velocity isrepresented by vg.
Vg
Particle
Vp
AIM OF EXPERIMENT
• To demonstrate diffraction phenomenon of electron to support wave character of material.
• This experiment gave establishment of quantum mechanics and schrodinger wave equation.
• The experiment consisted of firing an electron beam from an electron gun directed to a piece of nickel crystal at normal incidence (i.e. perpendicular to the surface of the crystal). The experiment included an electron gun consisting of a heated filament that released thermally excited electrons, which were then accelerated through a potential difference giving them a certain amount of kinetic energy towards the nickel crystal.
• To avoid collisions of the electrons with other molecules on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, an electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only elastically scattered electrons.
• As Max von Laue proved in 1912 the crystal structure serves as a type of three dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array,Bragg'slaw
• for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel.
This is 3-d grating of nickel target where scattering of electron takes place.
• By varying the applied voltage to the electron gun, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle θ = 50° with a voltage of 54 V, giving the electrons a kinetic energy of 54 eV.
• So this experiment proved de-brogliehypothesis and braggs equation.this also brought revolution in quantum mechanics.